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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 793-807
http://dx.doi.org/10.1155/S0161171282000738

Absolute continuity, singularity and product measures

Department of Mathematics, Washington State University, Pullman, Washington 99164, USA

Received 25 May 1982

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Conditions are given under which a product of two semifinite measures is absolutely continuous or weakly singular with respect to another product of two semifinite measures. A Lebesgue type decomposition theorem is proved for certain product measures so that the resulting measures are themselves product measures.